I was recently asked if Super 16mm film was capable of a higher resolution than 4K digital capture. Or, verbatim, the question was “also is 16mm a higher resolution than 4K [?]”. So, we have an opportunity to discuss the common confusion between raster and resolution.
Resolution is a measurement or a perception of how much discernible visual information appears in an image. It involves your entire imaging and display chain, not simply your capture medium. Resolution is measured in line pairs per millimeter.
The lens you're shooting with is capable of resolving a certain amount of information, your capture medium (sensor or film stock) is capable of resolving a certain amount of information, and your display or projection format is capable of resolving a certain amount of information. All of those things contribute to the 'resolution' of the viewed image.
'4K' is not a resolution, it is a raster size (meaning pixel or photosite dimensions, like 4096 x 2160, for example, or 1920 x 1080). It is extremely common both in camera (and display) marketing and in amateur cinematography circles to conflate the idea of raster with resolution. The two ideas are independent, and a given raster can “contain” a wildly varying amount of resolution.
If you were to compare lenses on the same capture medium (let's say the Alexa 65), you can produce very different resolutions at the same raster size. That is to say, both a very soft lens and a very sharp lens can be used when imaging to a 4K raster, but both the measured and the perceived resolution will be very different. Or, let's imagine you're shooting with a Master Prime, one of the measurably sharpest lenses available, and recording a 4K raster. What's your resolution when you throw the lens completely out of focus? It’s also common to use diffusion filtration to reduce the resolution of the system, usually for aesthetic reasons.
The perceived sharpness that a film stock is capable of rendering is described by a Modulation Transfer Function which plots how many line pairs per millimeter the stock is capable of discriminating at an acceptable level of contrast between the lines (i.e., can you actually distinguish between a black and white line, or is the image a gray mush?). 50% MTF tends to be the cutoff of acceptability. The MTF of film emulsion changes independently per dye layer, with the layers tending to diverge from each other between 10 and 20 lppm. The resolution of Kodak 500T at 50% MTF starts to decline steeply after 30-50 lppm, depending on the dye layer. Here is Kodak’s MTF chart for 5219/7219:
taken from https://www.kodak.com/content/products-brochures/Film/VISION3_5219_7219_Technical-data.pdf
At 30 lppm each line is 1/60mm, or 16.7 micrometers, wide.
The Alexa's photosites are 8.25 micrometers in diameter, or roughly 1/125mm. At first glance this would seem to say that the Alexa sensor can resolve about twice the information as 500T film stock, but let's not forget our friend Nyquist, who tells us that we need to sample our information at double the highest frequency of that information, so this gets us back to being able to resolve lines about 1/60mm wide again. With the slight blur from the OLPF, the actual resolution at 50% MTF is probably roughly equivalent to 500T film negative, but in the sensor's favor that resolution should be roughly constant across the R, G and B-masked photosites, unlike the variable resolution of film's three dye layers.
But that's not all! We have to take into account the enlargement of the medium when displayed or projected. Why does 16mm film look both grainier and softer than 35mm of the same emulsion when projected? Because to fill the same size screen (or monitor), the 16mm film frame must be enlarged (blown up) much more than than the 35mm film frame. The same is true when scanning film; there's still a relative size difference between a 16mm film frame and the scanner's imager that's greater than that between a 35mm film frame and the scanner's imager. A similar effect happens if you're comparing 16mm film which has been scanned to a 4K raster vs. a digital image captured at a 4K raster from a Super-35 sized sensor. When viewed on the same display the 16mm film scan will appear softer and grainer than the digitally captured image (assuming a low amount of noise in the digital image).
So, to sum up, it is highly likely that a 4K-raster digitally captured image will be perceived to have a higher resolution than 16mm film scanned to a 4K raster.